Question

for some positive integers m find the form in which every positive odd integer can be written
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Answer 1

Answer:

(c) We know that, odd intergers are 1,3,5,...

So, it can be written in the form of 2q + 1.

where, q = integer = z

or q = ...,-1,0,1,2,3,...

∴ 2q + 1 = ...,-3,-1,1,3,5,...

Alternate method

Let 'a' be the given positive integer .On dividing 'a' by 2, let q be the quotient and r be the remainder. Then, by Euclid's division algorithm, we have

a = 2q + r, where 0 ≤ r < 2

⇒ a = 2q + r, where r = 0 or r = 1

⇒ a = 2q or 2q + 1

when a = 2q + 1 for some integer q, then clearly a is odd

Answer 2

Answer:it is odd

Step-by-step explanation: